Publication:
Quotients of values of the Dedekind Eta function

Placeholder

Departments

School / College / Institute

Program

KU-Authors

KU Authors

Co-Authors

Xiong, Maosheng
Zaharescu, Alexandru

Publication Date

Language

Embargo Status

Journal Title

Journal ISSN

Volume Title

Alternative Title

Abstract

Inspired by Riemann's work on certain quotients of the Dedekind Eta function, in this paper we investigate the value distribution of quotients of values of the Dedekind Eta function in the complex plane, using the form eta(A(j)z)/eta(A(j-1)z), where A(j-1) and A(j) are matrices whose rows are the coordinates of consecutive visible lattice points in a dilation X Omega of a fixed region. in R-2, and z is a fixed complex number in the upper half plane. In particular, we show that the limiting distribution of these quotients depends heavily on the index of Farey fractions which was first introduced and studied by Hall and Shiu. The distribution of Farey fractions with respect to the value of the index dictates the universal limiting behavior of these quotients. Motivated by chains of these quotients, we show how to obtain a generalization, due to Zagier, of an important formula of Hall and Shiu on the sum of the index of Farey fractions.

Source

Publisher

Springer

Subject

Mathematics

Citation

Has Part

Source

Mathematische Annalen

Book Series Title

Edition

DOI

10.1007/s00208-008-0228-1

item.page.datauri

Link

Rights

Copyrights Note

Endorsement

Review

Supplemented By

Referenced By

0

Views

0

Downloads

View PlumX Details